DESIGN REHABILITAT INVESTIGAT E E Progressive Collapse Resistance

DESIGN REHABILITAT INVESTIGAT E E Progressive Collapse Resistance Competition entry by, Simpson Gumpertz & Heger Ömer O. Erbay & Ahmet Çıtıpıtıoğlu 25 April 2008 www. sgh. com

Objective • The objective of this investigation was to predict the progressive collapse response of a 1/8 th scale reinforced concrete frame, which was designed and tested by Northeastern University, using analytical methods. © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Frame Design • The reinforced concrete frame is the exterior frame of a building located in Memphis, TN (Seismic Category D). • Designed and detailed to satisfy ACI-318 integrity and special moment frame requirements. • Loads: – – LL = 70 psf DL = 100 psf (including the partitions) Exterior nonstructural walls: 100 plf Total weight of the building for seismic calculation = 2770 kips © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Reinforcement Detail (Full-scale Frame) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Reinforcement Detail (Test Frame) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Test Frame Glass Column © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Competition Questions • What will be the maximum dynamic displacement after column removal? • What will be the displacement after system becomes stationary after column removal? • Will there be any rebar rupture after column removal? • If the frame does not collapse after column removal, how much load can it sustain before failure? • What will be the failure mode and failure sequence? • Where will be the first rebar rupture? © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Challenges • Cannot make conservative assumptions – Need to precisely estimate the response • Unknown parameters: – Unknown bond characteristic between reinforcement and concrete – Uncertain concrete properties – Uncertain construction quality • Representing loading sequence; dynamic and then quasi-static pull down • Developing a model that can always converge without user intervention © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Method of Approach • Detailed Model: Continuum plane stress model to capture localize failure mechanisms, concrete cracking, rebar slippage, and shear failure • Parametric Model: Lumped-plastic-hinge model with beam elements, used for parametric analyses to determine the distribution of response quantities © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Continuum Model Concrete 2 D Solid Elements Reinforcement Truss Elements § Concrete: – 2 D Continuum Plane Stress elements with Reduced Integration. – Concrete damaged plasticity with tension stiffening to model post cracking rebar slippage. § Wire rebar: – Embedded Truss elements. – Rate independent metal plasticity with calibrated hardening. § Self weight and point mass Detailed Continuum Model © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Modeling Concrete Behavior (1) § Smeared Cracking” : cracks enters into these calculations by the way in which the cracks affect the stress and material stiffness associated with the integration point. § Cracking is assumed to occur when the stress reaches a failure surface that is called the “crack detection surface” Image taken from ABAQUS manual © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Modeling Concrete Behavior (2) § Concrete behavior is considered independent of the rebar § Rebar/concrete interface, such as bond slip and dowel action, are modeled by “tension stiffening” to simulate load transfer across cracks through the rebar § “Shear Interlock”: as concrete cracks, its shear stiffness is diminished. § Shear modulus is reduced as a function of the opening strain across the crack. Images taken from “Reinforced Concrete Mechanics and Design” by Mac. Gregor J. G. and Wight J. K. 2005 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Modeling Concrete Behavior (3) § In the absence of data to calibrate bond slippage “tension stiffening” was modeled as strain softening after failure reducing the stress linearly to zero at a total strain of 5, 10, and 15 times the strain at cracking © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Parametric Frame Model Distance from column centerline to the location of plastic hinge, dp Rigid plastic hinges (M-qp) Effective length of plastic hinge, lp Rigid offsets Spring for stabilization © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential Elastic beam elements

Modeling and Model Parameters (Cont. ) Beam Section Parameters Effective depth to top or bottom reinforcement, deff Plastic Hinge Parameters (lumped plastic hinge model) M M M k 2 k 3/lp k 1 f Moment – Curvature From section analysis using RESPONSE 2000 fp Moment – Plastic Curvature Derived from Moment – Curvature © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential qp Moment – Plastic Rotation Derived from Moment – Plastic Curvature relationship

Uncertain Parameters • Plastic hinge locations, dp – Uniform – 1. 25”-6. 25” where there is extra #7 (f 0. 110”) rebar at the connection 1. 25”-2. 5” where there is no extra #7 (f 0. 110”) rebar at the connection • Plastic hinge length, lp – Uniform – 0. 5 db – 0. 75 db • Yield and ultimate moment capacities, My & Mu – Uniform – 0. 90 -1. 15 times the nominal values • Initial and post yield stiffness, ki, ky – Uniform – 0. 90 -1. 10 times the nominal values • Elastic modulus of concrete, Ec – Uniform – 0. 95 -1. 05 times the experimentally tested values © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Loading Sequence Apply gravity (self weight of frame and attached masses) Continue analysis to damp-out dynamic effects Remove center column in 0. 05 s Load magnitude Continue analysis to damp-out dynamic effects (check whether the frame has collapsed or not) If frame not collapsed switch to static analysis Unload attached masses Pull down on center column 0. 2 4. 0 0. 305 0. 3 Dynamic Analysis 5. 0 6. 0 7. 0 8. 0 Static Analysis © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential Time, s

Dynamic Displacement Time-History of the Center Column Calculated Displacement Time-History Measured Displacement Time-History Peak Dynamic Displacement Calculated (Mean) Measured 0. 4 in. (10 mm) 0. 22 in. (5. 6 mm) Peak Static Displacement Calculated (Mean) Measured 0. 3 in. (7. 6 mm) 0. 20 in. (5. 1 mm) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Analytically Calculated Crack Locations after Column Removal © 2007 Simpson Gumpertz & Heger Inc.

Cracking at Beam-Column Joint § Model able to determine location and pattern of first

Most Probable Failure Sequence © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Most Probable Failure Sequence 12 11 9 6 1 2 10 7 3 4

Location of First Visually Observed Crack © 2007 Simpson Gumpertz & Heger Inc. Proprietary

Pull Down Test (at 3. 5 in. Displacement) © 2007 Simpson Gumpertz & Heger

Pull Down Force-Displacement Curve (Frame Model) Calculated Pull-Down Force-Displacement Curve Measured Pull-Down Force-Displacement Ultimate Pull-Down Force Measured 1800 lb Calculated (Mean) 2000 lb (frame model) 1700 lb (continuum model) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Summary of Results Comparison • What will be the maximum dynamic displacement after column removal? Measured: 0. 22 in. Calculated: 0. 4 in. • What will be the displacement after system becomes stationary after column removal? Measured: 0. 20 in. Calculated: 0. 3 in. • Will there be any rebar rupture after column removal? Measured: No Calculated: No • If the frame does not collapse after column removal, how much load can it sustain before failure? Measured: 1800 lb Calculated: 1700 lb - 2000 lb • Where will be the first rebar rupture? Measured: Grid D-2 Calculated: Grid B-2 or D-2 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Concluding Remarks § Analysis results are extremely sensitive to rebar bond slippage modeling. § Predicted excessive permanent displacements due to rebar slippage, compared to measured -0. 2 inches : – -1. 7 inches using 15 x et – -8. 8 inches using 10 x et § Initial pilot test frame built with plain wire reinforcement (no ribs) resulted with displacements within captured range in the continuum model where rebar slippage was considered. § More detailed modeling possible, but requires more data for more parameters to be calibrated. § More data may introduce more uncertainty and the problem may become unmanageable. A sensitivity analysis can be used to eliminate parameters that do not significantly affect the response parameters. © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential